It's possible the Changeling society does not have members at all. Quite possibly, it's just a single organism that, when Linked, has only a single mind. A mind that can undergo introspection and internal dialogue, sure, but still just a single mind.

Whenever a glob of goo leaves the Link, it starts to exhibit isolated thought processes. But those are absorbed into the whole as the glob returns; if a lot of "individuality" has been accumulated, as with Odo and the rest of The Hundred, it just takes a bit longer.